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A shortcut from broadband to spectral aerosol optical depth

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Proceedings of the Estonian Academy of Sciences, 2012,
61
, 4, 266–278
266
Proceedings of the Estonian Academy of Sciences, 2012,
61
, 4, 266–278
doi: 10.3176/proc.2012.4.02 Available online at www.eap.ee/proceedings
A shortcut from broadband to spectral aerosol optical depth
Martin Kannel
a*
, Hanno Ohvril
a
, and Oleg Okulov
b
a
Institute of Physics, University of Tartu, Ülikooli 18, 50090 Tartu, Estonia
b
Estonian Meteorological and Hydrological Institute, Mustamäe tee 33, 10616 Tallinn, Estonia Received 29 March 2011, revised 2 April 2012, accepted 27 April 2012, available online 20 November 2012
Abstract.
The concept behind the shortcut idea is a close correlation between column broadband aerosol optical depth (BAOD) and aerosol optical depth at 500 nm (AOD500). The method uses only two input parameters: (a) the Bouguer broadband coefficient of column transparency for optical mass
m
= 2 (solar elevation about 30°) and (b) integrated column precipitable water vapour which can be roughly estimated using surface water vapour pressure. In creating the method, a large database, including almost 20 000 complex, spectral and broadband direct solar beam observations at Tõravere, Estonia, during all seasons of a 8-year period, 2002–2009, was used. The AOD500 observations were performed by the NASA project AERONET and the broadband direct beam ones by the Estonian Meteorological and Hydrological Institute. Analysis of this database revealed a high correlation between BAOD and AOD500 which enabled transition from broadband to spectral AOD. Almost 82% of the observations in the database belonged to lower turbidities when AOD500 < 0.2. The root mean square deviation (RMSD) for AOD500 prediction in this range was 0.022. For AOD500 = 0.2–0.4, the RMSD was 0.035, for 0.4–0.6, the RMSD was 0.042. Relative RMSD for these ranges was about 22%, 12%, and 9%, respectively. For AOD500 > 0.6, relative RMSD remained 9%. For comparison, the same database was used to test Gueymard’s broadband parameterization based on his SMARTS2 classic model. The last one, apparently due to problems with circumsolar radiation, slightly but systematically underestimated the AOD500. However, there was a close correlation between our shortcut results and Gueymard’s broadband parameterization.
Key words:
AERONET, aerosols, aerosol optical depth, light attenuation, atmospheric integral transparency coefficient, broadband direct irradiance.
1. INTRODUCTION
*
Spectral aerosol optical depth of the atmospheric column, or extinction coefficient due to aerosol particles, AOD
λ
, is a central quantity in optics of atmospheric aerosols. It is usually measured with a multispectral instrument, sunphotometer, at a number of wavelengths, commonly including
λ
= 500 or 550 nm. There are two reasons for the AOD
λ
use. First, this parameter informs about turbidity of the atmospheric column. Second, dependence of AOD
λ
on wavelength
λ
is inversely related to size distribution of aerosol particles. Due to high initial cost sunphotometers are ex- pensive to obtain. Also their maintainance, because of regular servicing, is expensive
−
annual filter changing and recalibration at mountain locations with cloudless sky, at high Sun and very clear, stable atmosphere. For
*
Corresponding author, martin.kannel@ut.ee
that reason, the net of sunphotometers was sparse until the end of the 1990s. The situation changed completely with the advent and expansion of the NASA huge AERONET project providing the scientific community with massive high-quality standardized global surface information on AOD
λ
(Holben et al., 1998). It should be underlined that until now, the AERONET informa-tion is free to download. Like several other global atmospheric projects
−
NAAPS, HYSPLIT, MODIS, etc.
−
the free use of data is generously funded by the US government and tax-payers. However, there are strong reasons to continue elaboration of alternative, mainly broadband evaluations for AOD
λ
. An example of this kind of necessity is retrospective (or prospective) retrieval of AOD
λ
for periods in the past (or future) decades when spectral measurements were not (or will not be) available. Another example is a quick AOD
λ
estimation for correction of satellite remotely sensed data for regions
M. Kannel et al.: A shortcut from broadband to spectral
267
where spectral solar observations are not available but the broadband ones are. Sometimes, during a later inspection of time series of AOD
λ
, the recorded data seem too large (over-estimated) for a certain period. As usual in solar radia-tion observations, a doubt arises about an undesirable object (insect, spider’s thread, trash, etc.) dwelling on or inside the instrument’s tube. When there was only one sunphotometer operating but at the same time broad- band direct beam was also recorded, an alternative AOD
λ
estimation, through broadband approach, makes available reliability evaluations of spectral observations. And obviously, sites, which have enjoined a free use of AERONET observations without starting up their own solar spectral instrumentation, should be prepared to decrease in the number of simultaneously monitoring autonomous photometers or even general completion or commercialization of the AERONET project. In Estonia, the AERONET CIMEL photometer began observations on 3 June 2002, at Tõravere (58°15
′
, 26°27
′
, 70 m ASL), on the territory of the Tartu– Tõravere Meteorological Station. The station is included into the Baseline Surface Radiation Network (Kallis et al., 2005). Simultaneous registration of both spectral and broadband irradiances provided the opportunity to create a joint, integrated database for AOD
λ
and broad- band parameters of atmospheric transparency (turbidity). For eight years, 2002–2009, our joint database includes 19 592 spectral-broadband solar direct irradiance and surface water vapour pressure observations. About 75% of observations were made in April, May, June, July, and August, 9% in September, 8% in March, 3.6% in October, and only 4.4% together in January, February, and November. Due to low Sun and calibrations no joint observations were made in December. We consider a slant atmospheric column with optical mass 2
m
=
(solar elevation 30),
≈ °
consisting of three successive layers: (a) an ideal, clean, and dry atmo-sphere which includes O
3
and NO
2
; (b) water vapour; and (c) aerosol particles. This consideration enables us to express extinction of the broadband direct beam using a product of individual transmittances of each layer and to calculate, as a residual term, broadband aerosol optical depth, BAOD2, at 2,
m
=
for each of the 19 592 joint observations. The plot of the obtained values of BAOD2 against AOD500 revealed a high parabolic correlation enabling a “shortcut” from AOD500 to BAOD2. To get an idea about the quality of the proposed broadband shortcut to AOD500, we applied Gueymard’s (1998) parameterization, based on his known SMARTS2 model. Apparently due to a wider than traditional field of view (FOV
10)
= °
of the Tõra-vere actinometer AT50, values of the broadband direct beam in our database are slightly overestimated in cases of larger aerosol turbidity. This explains slightly under-estimated AOD500 as predicted by Gueymard’s para-meterization. Despite this systematic difference, there was a very high consistency (coherence) between both predicted results, expressed by the coefficient of determination,
2
0.994.
R
=
2. A THREE-LAYER STRUCTURE OF COLUMN BROADBAND TRANSMITTANCE
Spectral content of the direct solar beam reaching the Earth’s surface is not equal during a day. Broadband characteristics, therefore, depend on solar elevation even in the case of stationary and azimuthally homo-geneous atmosphere, causing the Forbes effect
−
virtual diurnal variation in atmospheric broadband optical characteristics (Ohvril et al., 1999). For this effect, even though spectral optical depth and related spectral optical parameters (transmittance, the Bouguer coefficient, etc.), are independent of optical mass
,
m
their broadband counterparts are not. Although there are no good solutions for strict transformation of column broadband optical parameters from one solar elevation to another, multiannual pyrheliometric time series, recorded at various stations, mainly on the territory of the former USSR, have stimulated creation of corresponding semi-empirical methods. Historically, a destination optical mass,
1,
m
=
was initially chosen (Kalitin, 1938). However, for control measurements the case where the Sun is at the zenith, is not available at most radiometric stations. The next integer number,
2
m
=
(solar elevation angle about
30),
°
was further preferred as a standard one in interpretation of pyrheliometric observations. A set of simple formulas links different broadband optical parameters like the Bouguer coefficient of transparency, transmittance, optical depth, the Linke turbidity factor (Ohvril et al., 2009). Concerning aerosol optics, the same reference air mass is also recommended (Gueymard and Kambezidis, 1997). We further limit the structure of extinction of the broadband direct solar beam by three processes or substances: (a) an ideal or clean and dry atmosphere (CDA), which includes Rayleigh scattering, absorption by ozone (O
3
), and nitrogen dioxide (NO
2
); (b) integrated column water vapour or precipitable water,
;
W
(c) atmospheric aerosol particles. Denoting their transmittances by
CDA,
τ
,
m
,
τ
,
Wm
and
aer,
τ
,
m
respectively, it is of considerable computational convenience to express the incident broadband beam irradiance at normal surface, “beam irradiance”, ,
m
S
as a direct product of individual beam transmittances which is equal to a presumption of three successive extinction layers (Gueymard, 1998):
Proceedings of the Estonian Academy of Sciences, 2012,
61
, 4, 266–278
268
0CDA,,aer,
τ τ τ
,
mmWmm
SS
=
(1) where
0
S
is the extraterrestrial broadband irradiance at the actual Sun–Earth distance, its average value, the “solar constant”, is 1.367 kW m
–2
(Lenoble, 1993). On the other hand, using broadband total trans-mittance,
τ
,
m
and the Bouguer coefficient of trans- parency,
m
p
(Kondratyev, 1969):
10
,
mmm
S pS
=
(2) we can also express
m
S
as
00
τ
,
mmmm
SSSp
= =
(3) which gives for broadband aerosol transmittance
aer,CDA,,
τ
.
τ τ
mmmmWm
p
=
(4) By similarity with Bouguer formula which, strictly speaking, is valid only for a monochromatic beam, the following equation defines broadband aerosol optical depth, BAOD
m
, which we denote in formulas by
aer,
δ
m
(Gueymard, 1998):
aer,aer,
τ
exp(
δ
).
mm
m
= −
(5) Combining this definition with (4), we obtain for BAOD
m
:
aer,aer,CDA,,
11
δ
ln
τ
ln,
τ τ
mmmmmWm
pmm
= − = −
(6)
aer,CDA,,
11
δ
lnln
τ
ln
δ
.
mmmWm
pmm
= − + +
(7) BAOD
m
is equal to the Unsworth–Monteith turbidity coefficient (Unsworth and Monteith, 1972; Gueymard, 1998). This parameter can be used to estimate aerosol contribution in attenuation of the broadband direct beam, in addition to a clean-wet atmosphere, consisting of CDA and water vapour only (Kambezidis et al., 1998). We now continue with 2
m
=
and have for BAOD2:
aer,22CDA,2,2
111BAOD2
δ
ln
τ
ln
τ
ln
τ
222
W
= = − + +
2CDA,2,2
1lnlnln
τ
.2
W
pp
= − + +
(8) Calculation of BAOD2 is now reduced to availability of three broadband quantities: (a)
2
τ
or
2
p
as results of broadband direct beam observations of
m
S
and following recalculations of
τ
m
to
2
τ
or
2
,
p
in order to go from optional
m
to a fixed one, 2;
m
=
(b)
CDA,2
τ
or
CDA,2
p
which should be calculated from models of ideal atmosphere, CDA; (c)
,2
τ
W
which first needs estimation of column precipitable water at zenith direction, ,
W
and, as a second step, calculation of transmittance of column water vapour for the entire slope column, 2.
m
=
There are two methods to obtain the Bouguer coefficient of transparency
2
p
from
m
S
observations, which both give close results (Ohvril et al., 1999). In Russia and Ukraine,
2
p
is calculated directly from the observed broadband direct beam ,
m
S
using the Evnevich–Savikovskij formula (Evnevich and Savi-kovskij, 1989):
sin0.20521.412
,1.367
hm
Sd p
+
=
(9) where
d
is the actual Earth–Sun distance in astro-nomical units. In Estonian actinometric practice the Bouguer coefficient of transparency, ,
m
p
is first calculated using Eq. (2). As a second step,
2
p
is recalculated from
m
p
using the formula that has been founded by Mürk and Ohvril (Myurk and Okhvril, 1990; Ohvril et al., 1999):
log0.009log1.8482
2.
m
pmm
ppm
+−
=
(10) Broadband coefficients of transparency,
CDA,2
τ
,
of a CDA, depend, besides molecular (Rayleigh) scattering, on absorption by trace gases, mainly by O
3
and NO
2
. For that, column amounts of trace gases should be first estimated.
3. EVALUATION OF COLUMN NO
2
AMOUNTS
Vertical NO
2
profiles as described by standard atmo-spheres usually refer to very clean areas without intensive combustion processes and therefore the column amounts are low. The 1976 U.S. Standard Atmosphere
−
USSA 1976 (Thomas and Stamnes, 2002) gives for the tropospheric (0–11 km) NO
2
column amount only 0.386
×
10
15
molecules cm
–2
. Normalizing this result with the Loschmidt constant (2.69
×
10
19
molecules cm
–3
, 0
°C, 1 atm), we obtain for the tropo-spheric NO
2
layer column thickness 1.4
×
10
–5
cm, which we denote, following Gueymard’s (1998) nomenclature, as 0.014 matm cm (
≡
0.014 DU). How-ever, this tropospheric NO
2
content seems to be considerably underestimated compared to present-day European values. Since the 1980s, the global mapping of column NO
2
has been possible with the help of satellites. Tropospheric NO
2
geography, with special focus on
M. Kannel et al.: A shortcut from broadband to spectral
269
Central and Northern Europe and the Baltic Sea Region, is given by Ionov (2010). His review, for 2004–2009, shows low tropospheric NO
2
for Estonia, (0.8
−
1)
×
10
15
molecules cm
–2
, or 0.03–0.037 matm cm. High tropo-spheric NO
2
values were found over St. Petersburg (up to 9
×
10
15
molecules cm
–2
or 0.335 matm cm), and even higher values over Belgium, Netherlands, Germany, and Moscow (up to 18
×
10
15
molecules cm
–2
or 0.669 matm cm). An extended review on stratospheric NO
2
global dis-tribution is given by Dirksen et al. (2011). For latitudes 25°–65° the NO
2
annual mean is about 3.2
×
10
15
molecules cm
–2
or 0.12 matm cm. The thinnest strato-spheric NO
2
layer is on the equator, 0.5
×
10
15
molecules cm
–2
or 0.019 matm cm. The amplitude of the seasonal cycle increases with latitude, with the largest stratospheric NO
2
column over the South Pole in summer, 6
×
10
15
molecules cm
–2
or 0.223 matm cm.
4. BROADBAND TRANSMITTANCES FOR SOME CDAs
In order to get a picture about variability of column transparency of ideal atmospheres with different O
3
and NO
2
contents, we made numerous runs of Gueymard’s (1998) parameterization. Table 1 shows three typical of them. Row 1 corresponds to very low concentrations: 150 DU (0.15 atm cm) for O
3
and only 88 pptv (10
–12
) for total NO
2
column amount. The ozone content of 350 DU (0.35 atm cm), in row 2, represents an annual mean for Estonia (Okulov, 2003; Okulov and Ohvril, 2010; Veismann and Eerme, 2011). The NO
2
amounts are also typical of this region. The table exhibits a relatively small sensibility of transparency and transmittance of different CDAs (the last three columns) to changes in column concentrations of trace gases. Considering now that the relative error of the observed (by an actinometer) broadband direct beam is
±
4% which leads to
±
2% errors in coefficients
2
,
p
we can assume that
CDA,2
ln0.1
p
≈ −
and rewrite (8) in a simpler form:
2,2
1BAOD2ln0.1ln.2
W
p
τ
= − − +
(11)
5. BROADBAND TRANSMITTANCE OF COLUMN WATER VAPOUR
In order to calculate the ability of solar radiation to pass the atmospheric water vapour, the amount of total column water vapour,
,
W
should first be estimated. The number of measurement techniques for
W
observations has increased considerably since the 1990s and now includes ground-based and space-borne optical sound-ings, microwave radiometry, as well as propagation delay estimation using ground-based GPS data. In most countries, however, the classic balloon-borne radio-sounding remains the main routine method for
W
monitoring (Jakobson et al., 2009), but the network of radiosonde stations is sparse and sondes are launched only 1
−
2 times per day. Therefore, especially for solar radiation and aerosol studies, correlation between
W
and surface meteorological parameters (mainly surface temperature and pressure of water vapour) is used. A short historical review of approximate calculations of
W
is listed by Okulov et al. (2002). For the Baltic region Jakobson et al. (2005) expressed seasonal means of
W
as linear functions of the geographical latitude degree. Suppose that the amount of
W
is already known. To investigate how
W
affects broadband transmittance through a hypothetical atmosphere consisting of water vapour only, we have to use some kind of radiative transfer model. However, there are two major problems: (a) the complexity of the extraterrestrial solar spectrum and (b) the peculiarity of the water molecule, leading to an extremely complicated vibration-rotation absorption spectrum (Maurellis and Tennyson, 2003). Nevertheless, during the last decades progress has been made in models calculating the water vapour attenuation of the broadband solar beam, leading to larger values of absorption. This statement follows, for example, from comparing parameterizations proposed by Zvereva (1968) and Gueymard (1995, 1998). For the calculation of extinction of broadband solar beam irradiance, we recommend the parameterization developed by Gueymard (1995, 1998), based on his SMARTS2 model. He used a solar spectrum of 1881 wavelengths, at 1-nm intervals within the most
Table 1.
Results of Gueymard’s (1998) parameterization runs to obtain broadband column transparencies (
p
CDA,2
and logarithm of it) and transmittances (
τ
CDA,2
) of ideal atmospheres with different O
3
and NO
2
contents NO
2
No. O
3
, atm cm tropos, atm cm stratos, atm cm tro+stra, atm cm tro+stra, pptv
p
CDA,2
ln
p
CDA,2
τ
CDA,2
1 0.15 0.000 03 0.000 04 0.000 07 88 0.9081
−
0.0964 0.8246 2 0.35 0.000 04 0.000 120 0.000 160 200 0.9042
−
0.1007 0.8176 3 0.60 0.001 00 0.000 200 0.001 200 1501 0.8998
−
0.1056 0.8096
Proceedings of the Estonian Academy of Sciences, 2012,
61
, 4, 266–278
270
important part of the spectrum (280–1700 nm). Although the method consists of 20 formulas, Ohvril et al. (2005) demonstrated that in a particular case, for atmospheric optical mass
2,
m
=
the transmittance of water vapour can be expressed by a single formula:
0.32,2
10.137,
W
W
τ
= −
(12) where
W
(cm) is precipitable water in the zenith direction. Plots of transmittances
,2
,
W
τ
calculated according to Zvereva (1968), Gueymard (1998), and Ohvril et al. (2005), are given in Fig. 1. Two results are evident: (a) approximation (12) provides an excellent agreement with Gueymard’s complicated parameterization
−
visually the two lower curves in Fig. 1 are difficult to distinguish from each other and (b) Gueymard’s method gives considerably stronger attenuation of direct solar beam irradiance than the model by Zvereva 30 years before. Broadband optical depths of water vapour:
,2,2
1
δ
ln
τ
2
WW
= −
are plotted in Fig. 2. As expected, Gueymard’s para-meterization, for
2,
m
=
can be successfully replaced by (12), but Zvereva’s model considerably under-estimates the optical depth of column water vapour. The curves of Gueymard and Ohvril et al., plotted in Figs 1 and 2, allow quick estimation of broadband trans-mittance and broadband optical depth of water vapour, at
2,
m
=
for any zenith precipitable water
.
W
For example, a planetary mean column humidity,
W
=
2.5
cm (Peixoto, 1992) corresponds to transmittance 0.82 and optical depth 0.10. Typical summer precipit-able water in the Baltic area, 2.0 cm, gives a trans-mittance of 0.83, and an optical depth of 0.094. During winter, at lower column humidity, transmittance and optical depth are more sensible to
W
changes (see
Broadband transmittance of water vapour,
m
= 2
0.700.750.800.850.900.951.00012345678910
Zenith precipitable water,
W
(cm)
T
r a n s m i t t a n c e ,
m
= 2
Zvereva (1968)Gueymard (1998)Ohvril et al. (2005)
Fig. 1.
Broadband transmittances of water vapour for optical mass
m
= 2 (solar elevation
≈
30°) as functions of precipitable water in the zenith direction,
W
.
Broadband optical depth of water vapour,
m
= 2
0.000.020.040.060.080.100.120.140.160.18012345678910
Zenith precipitable water,
W
(cm)
O p t i c a l d e p t h
Ohvril et al. (2005)Gueymard (1998)
Zvereva (1968)
Fig. 2.
Broadband optical depths of water vapour for optical mass
m
= 2 (solar elevation
≈
30°) as functions of precipitable water in the zenith direction,
W
.
Figs 1 and 2), but the average diurnal peak-to-peak (PtP) changes in
W
are usually low, e.g. in the Baltic region, PtP = 0.64 mm for summer and only 0.2 mm for winter. Of course,
W
can show fast variations, reaching up to 5 mm h
–1
during several hours, but exclusively during changes in the synoptic situation and substitution of airmasses above the location of observation (Jakob-son et al., 2009). We should not worry about these transitional cases, because, as a rule, cloudiness restricts observations of direct solar beam during synoptic changes. Substitution of (12) into (11) gives the final equation for BAOD2:
0.322
1BAOD2ln0.1ln[10.137],2
pW
= − − + −
(13) where zenith
W
is in centimetres. This formula is one of the main results of the given work. Below it will be used for transition from BAOD2 to AOD500. Figure 3 gives a visual review about limits of the extent of BAOD2 as a function of
2
p
and
.
W
As input we have used five values for precipitable water. The
Broadband aerosol optical depth,
m
= 2
0.00.10.20.30.40.50.60.70.80.40.50.60.70.80.9
Coefficient
p
2
B A O D 2
W
= 0.1 cm
W
= 1.0 cm
W
= 2.5 cm
W
= 4.0 cm
W
= 6.0 cm
Fig. 3.
Broadband aerosol optical depth as plotted against the broadband column transparency coefficient. Calculations are implemented for
m
= 2 and a set of values of zenith precipitable water, from
W
= 0.1 to 6.0 cm.

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